EPP spitzenkandidat Weber is by far bookies' favourite with odds of 1/1 (50%), although Barnier is in second place at 6/1 (14.3%), which came after his odds were slashed by nearly a third since November 2018, according to Ladbrokes.
In the wake of the European Parliamentary elections, attention turned to who would replace Jean-Claude Juncker in Brussels' top job as EU Commission president.
The balance of power had clearly shifted away from traditional parties, which only held on to top spots by a slim margin.
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Euronews' Political Editor Darren McCaffrey explained that everything hinges on a high level EU meeting on Tuesday to work out a process for choosing the commission head and whether the spitzenkandidat process will be abandoned.
If the system is upheld one of the lead candidates from the four top performing parties — Manfred Weber (EPP), Frans Timmermans (S&D), Margrethe Vestager (ALDE), Ska Keller (Greens) — is most likely to take office.
Per the spitzenkandidat system, the leader of the European party that commands the largest coalition after the election is likely to become the Commission president.
If it is thrown out, candidates that were not nominated spitzenkandidat could come to the fore, including the EPP's Michel Barnier and Kristalina Georgieva.
The process has highlighted a divide between the bloc's heads of state and thus could be scrapped with French President Emmanuel Macron speaking out against it as well as Luxembourg Prime Minister Xavier Bettel who called it a "stupid idea".
Who are bookies backing?
The EPP's Weber is by far bookies' favourite at even odds, although Barnier is in second place at 6/1 (14.3%), which came after his odds were slashed by nearly a third since November 2018, according to UK bookmakers Ladbrokes.
Weber remains firm favourite, but his probability of becoming the next Commission president has gone down from 4/5 in November 2018.
The EPP candidates are followed by Timmermans at 8/1 and Vestager at 10/1.
Who could realistically command a majority?
"It will be interesting to see whether the Liberals will prevail over the EPP and Social Democrats as the latter two no longer have a majority and they will need to reach out to a third force," Dídac Gutiérrez Peris, professor of European Affairs at Sciences Po Paris, told Euronews.
While Manfred Weber was the clear favourite, with this level of fragmentation, there will more names on the table than first expected, he explained.
"I think that the European Council in recent summits has had a very clear message that the President of the European Commission had to be a woman and this is going to have a clear impact," the professor added.
He thinks liberal Margrethe Vestager and other experienced female politicians could attain to the presidency.
Indeed, McCaffrey agrees that while Vestager has an uneasy relationship with Macron, which could work against her, she could swing his backing and the bloc is under pressure to put a woman in the top spot in either the Commission or Council.
Any outside candidates
Dutch Prime Minister Mark Rutte has repeatedly sought to squash speculation that he could become commission president, saying he wants to finish his term as Dutch prime minister, nevertheless, Rutte is tipped as a potential candidate and appears in Ladbrokes' list, albeit at 20/1.
While she is a "massively outside bet" according to McCaffrey, Merkel — whose centre-right CDU party is part of the EPP group — is on her way out as German chancellor but remains a very unlikely choice for the top job.
If the process of finding a president becomes too difficult, there have also been rumours Juncker's term could be extended, although it took three attempts for current President of the European Council Donald Tusk to be appointed and that was in a less fractured parliament, he added, so this remains extremely improbable.